伴随的区间收费公路性质
The interval turnpike property for adjoints
摘要：
在这项工作中，我们推导出一个区间收费公路的状态和控制的假设下，有限维和无限维非线性最优控制问题的伴随区间收费公路的结果。我们考虑由满足谱分解条件的有限维不稳定部分的半群的生成元所控制的可镇定动力学，并在一阶最优性条件的连续性假设下证明了所需的收费公路性质.我们进一步给出了解析半群的强估计，并给出了一个边界控制半线性热方程的数值例子来说明结果。
英文摘要：
In this work we derive an interval turnpike result for adjoints of finite- and infinite-dimensional nonlinear optimal control problems under the assumption of an interval turnpike on states and controls. We consider stabilizable dynamics governed by a generator of a semigroup with finite-dimensional unstable part satisfying a spectral decomposition condition and show the desired turnpike property under continuity assumptions on the first-order optimality conditions. We further give stronger estimates for analytic semigroups and provide a numerical example with a boundary controlled semilinear heat equation to illustrate the results.
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